Bayes' Theorem Example: Surprising False Positives

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  • Опубліковано 25 лис 2024

КОМЕНТАРІ • 162

  • @ccuny1
    @ccuny1 4 роки тому +52

    What happens when you're 58 and you decide to (re)learn discrete math, logic and probabilities? You watch this series and have a fun ride. Liked and subbed: it's brilliant, lively, entertaining and a great (re)learning experience. Thank you so much.

  • @jayare6975
    @jayare6975 3 роки тому +19

    the best part is how it goes in a bit further depth by exploring what happens if you test positive twice ( probability of disease given you test positive 2 times in a row )
    that ish hit different

  • @jackwillims4248
    @jackwillims4248 4 роки тому +41

    This global pandemic is the perfect time to learn this theorem

    • @DrTrefor
      @DrTrefor  4 роки тому +10

      For sure, if there was ever a more perfect application it is hard to imagine

    • @Explorer982
      @Explorer982 3 роки тому +2

      Yup. The amount of arguments i have had with people who claim vaccinated and unvaccinated are both spreading covid equally...ignoring all the vaccinated who did not get infected in the first place and so were not in the studies....

    • @VndNvwYvvSvv
      @VndNvwYvvSvv 2 роки тому

      First by examining how the results were games by manipulating cycle thresholds and changing the criteria for a "positive" to include similar symptoms of any illness, the suddenly "died with" as opposed to "died from" most of while had 4+ comorbidities becomes quite shocking. The only remaining question is at what confidence interval we can deem it a for-profit scam with CEOs and board members of oversight approving their own profits. Whoops!

  • @juanchetumare
    @juanchetumare 2 роки тому +5

    I agree with the majority of the comments. This was masterfully explained. I used to be a TA on discrete maths, probability and statistics and this felt like a breath of fresh air. Thanks a lot!

  • @renelchesak3555
    @renelchesak3555 5 років тому +7

    Beautiful wrapping up of the concept! "The whole point of Bayesian analysis is that as I get more information, I get to update the probabilities by which I believe events are going to occur."

  • @ralphmachado8201
    @ralphmachado8201 4 роки тому +20

    Today you thought me something in 12 minutes which my teachers couldn't teach in 12 months.!

  • @alexjohnston6847
    @alexjohnston6847 4 роки тому +12

    Worth explicitly showing are the relationships of TP (True Positive), TN (True Negative), FP (False Positive), and FN (False Negative). These relationships are often glossed over, and people frequently mix them up, leading to wrong answers! True Positive and False Positive are NOT complements, nor are True Negative and False Negative. Instead, the TP/TN/FP/FN relationships are:
    1. TP and FN are complements, so TP = 1 - FN and FN = 1 - TP
    2. TN and FP are complements, so TN = 1 - FP and FP = 1 - TN

    • @muhammadsiddiqui2244
      @muhammadsiddiqui2244 3 роки тому +1

      Thanks, I was confused about them.

    • @VndNvwYvvSvv
      @VndNvwYvvSvv 2 роки тому +1

      Yes, and even worse then they claim a certain reliability but then increase and decrease cycle thresholds to make big numbers, then to "prove" their product is after self-appeoving it with nepotistic relationships. ;)

    • @seyedhamidazimidokht3569
      @seyedhamidazimidokht3569 Рік тому +1

      I found This more intuitive:
      TP + FN = Total Positive ==> TP = Total Positive - FN. (this was mentioned in the video. getting %90 from %10).

    • @farmanshaik445
      @farmanshaik445 18 днів тому

      @@seyedhamidazimidokht3569I still don’t get why TP + FP = Total positive is not true

    • @farmanshaik445
      @farmanshaik445 18 днів тому

      Like, you got tested positive, and it means that 5% you don’t have the disease right, and 95% you have it

  • @yehuawang7553
    @yehuawang7553 Рік тому +1

    last year you saved my calculus course this year you are saving my statistic course

  • @michaeldeleted
    @michaeldeleted 2 роки тому +4

    I have watched at least 10 other videos on Bayes. After watching yours I finally get it. Thanks, so much!

  • @DK-ij9sh
    @DK-ij9sh Рік тому +1

    All the lessons about Bayes' Theorem are great. Thanks for explaining them in a simple and interesting way.

  • @geeves21312
    @geeves21312 5 років тому +1

    This is exceptionally well explained.
    I have real trouble assigning the events. For example, "P(A|B) means have disease having tested positive, and P(B) is testing positive)". The breakdown has really helped wrap my mind around it.
    Thank you!

  • @simonhwang4
    @simonhwang4 4 роки тому

    Your enthusiasm for teaching math is simultaneously disturbing and infectious. Thanks for the work you do

  • @sakura-sc5bw
    @sakura-sc5bw 4 роки тому +10

    I was really struggling with this theorem. Your video helped tons. Thanks a lot!

    • @DrTrefor
      @DrTrefor  4 роки тому +2

      You're very welcome!

  • @aravkat
    @aravkat 3 місяці тому

    Best video I have watched to get an intuition for Bayes theorem. Thank you!

  • @Samirkantadas123
    @Samirkantadas123 2 роки тому

    Sir ...what a power of explanation, confidence you have..
    Thank you so much sir..

  • @nurulanasuhahseffene4887
    @nurulanasuhahseffene4887 3 роки тому +2

    you have a great way of explaining things and this is random but you sound like ryan gosling

  • @harshmodi2553
    @harshmodi2553 4 роки тому

    Sir, Your explanation about the concepts are so clear that anyone can understand clearly. Thank you so much.

  • @danielgoldberg7727
    @danielgoldberg7727 2 роки тому +1

    Doctor you are the best. Thanks for breaking this down for mr.

  • @kunalbhatt4333
    @kunalbhatt4333 Рік тому

    WONDERFULLY EXPLAINED CONTENT...I'm surprised this has so few views...
    Well he has a huge no of subscribers...so that makes sense
    thanks!

  • @AJP0987654321
    @AJP0987654321 4 роки тому

    I think you need more explanation going from the original formula to the expanded denominator, but it's a great example and helped me dearly. Thank you very much

  • @alice20001
    @alice20001 5 років тому +2

    Thank you so much for putting in the second scenario where you go through the test twice!

  • @sdsa007
    @sdsa007 2 роки тому

    Bravo! gotta update my prostate-cancer probability!

  • @justus4883
    @justus4883 3 роки тому +1

    Thanks, had only been given a week to understand this theorem and your videos really help my understand it 👍

  • @andrewharrison8436
    @andrewharrison8436 Рік тому

    The importance of knowing your initial risk (and how it differs from the population incidence) can't be stressed enough.
    When I see my doctor it is because something is wrong. The doctor looks at the presentation and effectively puts me in a sub population with an elevated risk of various diseases - the results of relevant tests then update those risks until there is enough confidence to prescribe a treatment. (Well that's the theory). In practice the diagnosis involves the doctors experience, training and judgement.
    Bayes theorem allows that subjective judgement to be replaced or at least reinforced by calculation.

  • @shivendrayadav5962
    @shivendrayadav5962 4 роки тому

    This principle has applications in information retrieval too.I was struggling to understand it but thanks to you I am out of the woods. Cheers mate

  • @thesouravmalakar8922
    @thesouravmalakar8922 5 років тому +16

    *Wow, excellently explained !! By the way, it's little like tongue twister !!*

  • @Asher_804
    @Asher_804 Рік тому

    Why I am thinking about Corona tests rn ?
    And word positive for it is haunting!

  • @PetukTraveller
    @PetukTraveller 4 роки тому +5

    Illness, diseases , these are the examples to understand Bays Theorem :)

  • @davidgarner5628
    @davidgarner5628 6 років тому +5

    The example of repeating the test assumes that the two tests are uncorrelated (independent). It is often the case that when a medical test fails to give the correct result, it is for a reason and repeating the test may fail for the same reason.

    • @Diagnoc
      @Diagnoc 2 роки тому

      That was also my concern.

  • @tigliodavoli932
    @tigliodavoli932 Рік тому

    Great! the best explanation I've ever heard

  • @markbole2496
    @markbole2496 2 роки тому

    Fun to watch in COVID times. Case numbers being reported using lateral flow could be far off.

  • @sunny739
    @sunny739 2 роки тому +1

    amazing explanation sir ! thanks a lot for this tutorial

  • @mustanserbillah2975
    @mustanserbillah2975 5 років тому +1

    superb method of teaching which every one can easily understand.
    thank you sir

  • @deepaaggarwal2812
    @deepaaggarwal2812 2 роки тому +1

    Very well explained, it helped a lot. Thanks.

  • @lfknight8014
    @lfknight8014 2 роки тому

    makes it seem like grade 6 content, so perfectly explained

  • @omerkzlaslan3712
    @omerkzlaslan3712 Місяць тому

    Excellent explanation. Thank you sir

  • @andrewharrison8436
    @andrewharrison8436 Рік тому

    Doing the test twice is not necessarily independent events. What is really needed is the chance that someone who hasn't the disease but had a false positive having a second false positive.
    Ideally the second test would be a different test for the same disease where the results are independent.

  • @hafizhabdillah3030
    @hafizhabdillah3030 4 роки тому

    better than my lecture, moreee better, you are the best. thanks for sharing, hope you be well, during this pandemic.

  • @jojorusinek7492
    @jojorusinek7492 4 роки тому +2

    i arrive at the same answer but my "priors" have changed on the second test. it appears that you use the same prior of 1% on the second test for the probability of having the disease notwithstanding the positive first test.
    post test odds = pre-test odds x likelihood ratio (LR) for +'ve test,
    where pre-test odds = .01/0.99 or .0101 and LR is sensitivity/(1-specificity).
    so, post test odds =0.0101x0.9/0.05
    = 0.181818
    probability = odds/(1+odds)
    = 0.181818/1.181818
    = 15.38%.
    for a second test, the pre-test odds are no longer 1%, but are .181818
    post-2nd test odds = 0.181818 x LR for a positive test (which has not changed)
    = 0.181818 x 0.9/0.05
    = 3.27
    probability = 3.27/4.27
    = 76.6%

  • @v8pilot
    @v8pilot 2 роки тому +3

    I found this video very helpful and I thank you for presenting it. However, does not the analysis for the case of testing positive twice in a row depend on an assumption that errors in the tests are independent? I can imagine situations where successive tests are far from independent - for example I might use covid test kits from the same production batch or there might be some peculiarity of my blood chemistry that routinely confuses some enzyme test.
    (I used to calculate reliability of communication networks. I found that even very small correlations between link failures could completely change results calculated on the assumption of independence between link failures.)

  • @domzippilli3738
    @domzippilli3738 6 років тому

    Great work, this helped me a lot. I see you just published this, and with the growth in popularity and relevance of probabalistic programming and machine learning, it's right on time.

    • @domzippilli3738
      @domzippilli3738 6 років тому

      As a side note, I heard a baby crying around 8 minutes... assuming that's yours, congratulations!

  • @WernerBeroux
    @WernerBeroux Рік тому

    The second part (taking the test twice) assumes that the events are independent. If it's something stable in the test subject's body that isn't the disease that triggers the false positive, then taking the test many times would have no affects on the probabilities.

  • @sunnys7899
    @sunnys7899 4 роки тому +1

    Outstanding explanation

    • @DrTrefor
      @DrTrefor  4 роки тому

      Glad it was helpful!

  • @Esther_Myrtle_Mate
    @Esther_Myrtle_Mate Рік тому

    I'll have to rewatch this a couple of times ✌️

  • @tingtingzhang5349
    @tingtingzhang5349 2 роки тому +1

    very helpful! Thank you so much!

  • @dddhhj8709
    @dddhhj8709 3 роки тому +1

    pretty good explaination

  • @ObaidurRehmanX
    @ObaidurRehmanX 3 роки тому +1

    Excellent way of teaching. Subscribing!

  • @rehabalsaleh166
    @rehabalsaleh166 3 роки тому +1

    Wow! I got it! Thank you so much!

  • @b.s.balakumarbalakumar867
    @b.s.balakumarbalakumar867 4 роки тому

    Excellent exposition

  • @ZEYNEPBESTECOŞKUN
    @ZEYNEPBESTECOŞKUN 3 місяці тому

    There are some things that I did not understand:
    1)Why are we dividing by P(B) 5:57
    2) Why is it that it is 90% of that 90%? What is the idea behind that?

  • @continnum_radhe-radhe
    @continnum_radhe-radhe Рік тому +1

    This is quite interesting.

  • @andyellingson8617
    @andyellingson8617 4 роки тому +1

    Thank you for the videos, very helpful

  • @chineduuchegbu1776
    @chineduuchegbu1776 Рік тому

    you explained this so well go off unc

  • @user23724
    @user23724 3 роки тому +1

    This was a great video, it really helped so much, thank you, you're really helping me love math! :)

  • @shivanibiswal3269
    @shivanibiswal3269 5 років тому +2

    Greatly explained.. thank you 😊

  • @fabiovargasbr
    @fabiovargasbr 2 роки тому +1

    Excellent

  • @rafamejia11
    @rafamejia11 4 роки тому +1

    I am wondering if someone could use a Bayesian approach to estimate undetected covid-19 cases?, I mean obtain the probability of infected population that are not being tested in a country or in a specific region. Especially on those places that the government is not given that much information about the spread of the virus, if in fact you can actually use Bayes' Theorem, can you make a video about that?

  • @joserobertopacheco298
    @joserobertopacheco298 2 роки тому

    Very good video, one of the best I have ever watched about this subject. But at 2:32 he should consider 10 % not 5%, as he said at 2:09 that the teste also have a false negative rate of 10%. May I be wrong?

  • @lovelyjain1568
    @lovelyjain1568 7 місяців тому

    thanx a lot....true life saver

  • @multipleoranges6307
    @multipleoranges6307 3 роки тому +1

    Thank you so much!

  • @BANKO007
    @BANKO007 Рік тому

    Great video. Shame there is so much boom and echo in the sound.

  • @santosksingh
    @santosksingh 6 років тому +2

    Awesome explanation!

  • @QZainyQ
    @QZainyQ 3 роки тому +2

    That's a baby crying or a cat at 8:10😂

    • @DrTrefor
      @DrTrefor  3 роки тому +1

      haha that's my baby:D

    • @QZainyQ
      @QZainyQ 3 роки тому

      @@DrTrefor That's beautiful, best wishes man,
      And you really have been of great help

  • @karannchew2534
    @karannchew2534 2 роки тому +2

    08:09 baby sound?

  • @simonndungu9746
    @simonndungu9746 5 років тому

    From past experience it is known that a machine if set up correctly 90% of the time, then 95% of good parts are expected but if the machine is not set up correctly then the probability of a good part is only 30%. On a given day the machine is set up and the first component produced was found to be good. What is the probability that the machine is set up correctly?
    solution for this?

  • @ŚmiemWątpić
    @ŚmiemWątpić 6 років тому +1

    Amazing! 😀😁😍😎
    Most underwatched video on youtube! 😐

    • @abinashgiri7528
      @abinashgiri7528 6 років тому

      Śmiem Wątpić because he stolen idea from Veritasium

  • @aneet84
    @aneet84 4 роки тому

    Well made video! I am a college professor and aspire to this level also but I have a few questions: (1) Do you get tired through having to be as expressive (this is a good thing!) as you are, through an online medium? I see that you make a great effort in projecting your voice and also gesticulating to drive home "the point". This must be tiring (2) What recording/capturing software do you use? Thank you for your time!

  • @shis10
    @shis10 4 роки тому

    Excellent video

  • @aminzaiwardak6750
    @aminzaiwardak6750 5 років тому

    Thanks a lot you explained very good.

  • @bnjaminhartley9141
    @bnjaminhartley9141 4 роки тому

    Make some videos on systems and signals

  • @kelvinle8662
    @kelvinle8662 2 роки тому

    I have a question:
    There is a store. 40% of the store contains products from company A, the remainder from company B. The store is also composed of 30% Large items, the rest being Small items. Suppose that 50% of the store is composed of items that are either from company B or is Large, what is the probability of choosing an item belonging to company A given that the item you chose is Small?
    So this is how I did it:
    P[B] = 40% so the other 10% must be the large items from company A to make P[B & L] = 50%. Which means that P[L|A] = (1/6) because 60% x (1/6) gives me the 10% I needed. This also means that P[S|A] = 5/6.
    Since company A supplies 10% of the Large items, this must mean that company B must supply 20% of the Large items to make a storewide total of 30%. Which means P[L|B] = (1/2) and P[S|B] = (1/2).
    Using Bayes' Theorem, I got P[A|S] = (1/2). Is this correct?

  • @charlesedeki--mathcomputer7198
    @charlesedeki--mathcomputer7198 4 роки тому +1

    Please what is the name of the software you are using for the video, its great way to present lecture, thank you.

    • @DrTrefor
      @DrTrefor  4 роки тому

      I have a whole vid about my process here: ua-cam.com/video/hmQd_P_qj1w/v-deo.html&ab_channel=Dr.TreforBazett

  • @pikeconsultinggroupinc.5287
    @pikeconsultinggroupinc.5287 2 роки тому

    Why don't you use the first test's posterior probability of 15.4% ,which then becomes a prior ,to figure out second test posterior probability?

  • @omerozgurcelik907
    @omerozgurcelik907 Рік тому

    This is great 👍

  • @legendaryplayer4486
    @legendaryplayer4486 4 роки тому

    Sir do you have a video regarding Bernoulli trials.

  • @emmablassel843
    @emmablassel843 4 роки тому

    Thank you.

  • @TheMainCOW
    @TheMainCOW 4 роки тому +2

    LOVE THE VIDEO! But, I think you confused FP with FN. If there is 10% chance that test will give a FN, then there is 90% chance that when test gives negative, we actually DO NOT have the illness. On the other hand, if there is 5% chance that test will give a FP, then there is 95% chance that when test gives positive we actually DO have the illness. So, P(A) should be 0.95, correct?

    • @suyash601
      @suyash601 4 роки тому +1

      Let me clear this a bit for you. I am restating your sentence with little modifications. If there is 10% chance that test will give a FN, then there is 90% chance that when test gives positive, we actually DO have the illness. On the other hand, if there is 5% chance that test will give a FP, then there is 95% chance that when test gives negative we actually DO NOT have the illness.

    • @liyah33
      @liyah33 4 роки тому

      When do we get answer to this question...

  • @websogooddotcom
    @websogooddotcom 4 роки тому +1

    The opposite is also true. If you don't have the disease and given the test is positive, the first test would yield 84.6% (approximately 5/6) probability of getting a false result. The second test would drop to 23.4%. Only the 3rd test would be close to zero (i.e 1.7%). Therefore most of the medical test/statistic is not trustworthy if taken only once. However, this is also true for the distributed data itself. Because IF all the 100 subjects are only tested once, how trustworthy is the distributed data that you depend on initially?

  • @crypticnomad
    @crypticnomad 4 роки тому

    How would one apply this concept to a model that is fairly well calibrated but has a pretty large false positive rate? Instead of just a binary output it gives a probability. Would I use that probability as the prior?

  • @zorba81674
    @zorba81674 4 роки тому +2

    Trevor, wouldn't we use 15.4% as the "priior" that you do have the disease when you run the test a 2nd time? I'm thinking of the posterior becoming the prior.

  • @Jimmy-wh1fd
    @Jimmy-wh1fd 6 років тому

    Very informative!

  • @kmf7102
    @kmf7102 2 роки тому

    I've love this video with just the numbers and formulas available while you explain instead of recalling numbers from 10 minutes prior. You waving your hands and being wild is pretty distracting. Thanks for your help with Bayes.

  • @karannchew2534
    @karannchew2534 Рік тому

    2:06 Why positive test might have cases?

  • @hardiksharma2838
    @hardiksharma2838 4 роки тому +4

    I'm corona infected,
    But now I'm not sure.

  • @pawanmishra9342
    @pawanmishra9342 6 років тому +1

    Great work

    • @pawanmishra9342
      @pawanmishra9342 6 років тому +4

      I don't know why people don't watch this work instead of pewdiepie

  • @hamedazimi2726
    @hamedazimi2726 Рік тому

    Thank you for your detailed explanation, but shouldn't it be 0.95 for P(B|A) instead of 0.9? Because P(B|A) represents the probability of a positive test result given that one is actually sick. With a 5 percent false positive rate, it means that 95 percent of sick people would receive a positive test result (which aligns with P(B|A) of 0.95). 7:41

    • @CarolKrein
      @CarolKrein 18 годин тому

      no! in that part you're just deducting the 10% probability of having a false negative

  • @luisbielmillan8467
    @luisbielmillan8467 3 роки тому +1

    ty ty ty, my teacher didnt explain shit throughout the course

  • @grumpywasp4533
    @grumpywasp4533 4 роки тому

    A genuine question. Doesn’t the FPR reset each time? Meaning every individual test has a 95% chance of being correct. This isn’t the same as 5 out of 100 being false.
    If the accuracy of every individual test is 95%, then each individual tests is 95% accurate. Does that in reality equate to 5 out of 100 being wrong? Can you apply specific accuracy to bulk testing?

    • @DrTrefor
      @DrTrefor  4 роки тому

      Indeed, there is a big difference between 95% and 5 in 100 people. The most likely outcome for 100 people is 5, but in any specific group of 100 people sometimes it will be less and sometimes more than this. So it is ok to build intuition like I did a the beginning of the video with a sample of 100 people, but you can't only look at that.

    • @grumpywasp4533
      @grumpywasp4533 4 роки тому

      Dr. Trefor Bazett thanks for this! I was having an argument about the COVID PCR FPR - 0.8% (ish). I argued that out of 100k tests if only 80 are positive then they could all be false as the PFR suggests around 800 FPs. I was told “no” that’s statistically highly improbable as the likelihood of each individual positive being correct is 99.2%.
      I don’t know how to reconcile the two - I’m not maths smart!

  • @kjeldgaard0
    @kjeldgaard0 4 роки тому +1

    I am puzzled at your calculation of P(A|B) after the second test. Instead of using the probability of testing positive twice, why don't you simply update the prior P(A) to be 0.154 instead of 0.01? Given that the first test is positive, the probability that the patient has the disease is no longer the general prevalance of 1% but is now 0.154. The sensitivity and specitivity of the test is the same, so you end up with P(A|B) = .74

    • @pikeconsultinggroupinc.5287
      @pikeconsultinggroupinc.5287 2 роки тому

      That's exactly my thought. the new (2nd test) prior is the 1st test's posterior probability 0f .154

  • @Gumikrukon
    @Gumikrukon 6 років тому

    Great stuff :) Thank you! :)

  • @humzahalkindi
    @humzahalkindi 4 роки тому

    Awesome

  • @RedditLeafy420
    @RedditLeafy420 4 роки тому

    I got tested positive for anphetamine and ecstasy but i havent used anything so what will happen, they told me that they will send the same urine again and contact me

  • @shilohmheespana7837
    @shilohmheespana7837 4 роки тому +1

    Hello sir, thanks for that clear explanation however i have one question. Should not we use the result of the first solving which is 0.154 as a prior for the 2nd test result where it resulted into another positive? Im new to this so I'm quite confused so please correct me on which part did i misunderstood. Thank you so much :D

  • @av6530
    @av6530 4 роки тому +1

    shouldn't be P(B|A)=.95? I'm confused on this part, other than that the video was amazing!

    • @jojorusinek7492
      @jojorusinek7492 4 роки тому +1

      false negative rate of 10% means than the test will reflect positive for the presence of the disease 90% of the time. The sensitivity of the test is .90 (will be positive when the disease is present).

  • @kashmoney1227
    @kashmoney1227 5 років тому +1

    What does the 77 percent represent

    • @MrTighe12
      @MrTighe12 5 років тому

      that you actually have the disease given you have just done the test twice and both times it came up positive

  • @DirtyPhlegm
    @DirtyPhlegm 6 років тому

    Suppper video!!

  • @jacksmith870
    @jacksmith870 4 роки тому

    Video by veritasium says the P(Having Disease) is prior information so it is updated using the previous result. But you updated P(Testing positive| Having Disease) . What am I missing here?

    • @jacksmith870
      @jacksmith870 4 роки тому

      found out there are two ways to get to the same answer. Either Update the prior probability or update the P(HD| test positive).

  • @bernardodc9631
    @bernardodc9631 2 роки тому

    I teste positive for covid, with 6% chance of false positive (and 96% true positive). Then tested negative twice. Wasn't able to crunch the numbers, though

  • @johhnyjoe5636
    @johhnyjoe5636 2 роки тому

    This is the most confusing and incoherent explanation I have ever heard for this scenario. Wow.

  • @danielc4267
    @danielc4267 5 років тому

    If you don't understand why True Positive + False Negative = 100%, check out this wikipedia picture:
    en.wikipedia.org/wiki/Sensitivity_and_specificity#/media/File:Sensitivity_and_specificity.svg